Nature of problem:Multi-loop integrals are needed for the evaluation of quantum
corrections. An important class of loop diagrams is covered by
so-called vacuum integrals which have no external momentum. MATAD can
analytically compute those one-, two- and three-loop vacuum integrals
where one mass scale is present.

Solution method:The method of integration-by-parts is used in order to obtain recurrence
relations which reduce complicated integrals to a small set of so-called
master integrals. They have to be evaluated once and for all. In
addition a user interface is provided which makes it easy to put in
complicated diagrams in a rather compact way.

Restrictions:The restrictions on the complexity are given by the hardware limitations
of the computer and the limits on the size of the storage files inside
FORM [1].

Running time:The runtime strongly depends on the complexity of the diagram under
consideration. It may vary from a few seconds to the order of a few
weeks.